The rstanarm package is an appendage to the rstan package, the R
interface to Stan. rstanarm enables many of the most
common applied regression models to be estimated using Markov Chain Monte Carlo,
variational approximations to the posterior distribution, or optimization. The
package allows these models to be specified using the customary R modeling
syntax (e.g., like that of glm with a formula and data.frame).
Additional arguments are provided for specifying prior distributions.

The set of models supported by rstanarm is large (and will continue to
grow), but also limited enough so that it is possible to integrate them
tightly with the pp_check function for graphical posterior predictive checks using bayesplot and the
posterior_predict
function to easily estimate the effect of specific manipulations of predictor
variables or to predict the outcome in a training set.

The fitted model objects returned by the rstanarm modeling functions are
called stanreg objects. In addition to all of the traditional
methods
defined for fitted model objects, stanreg objects can also be used with the
loo package for
leave-one-out cross-validation, model comparison, and model weighting/averaging
and the shinystan
package for exploring the posterior distribution and model diagnostics
with a graphical user interface.

Check out the rstanarm vignettes
for examples and more details about the entire process.

The model estimating functions are described in greater detail in their
individual help pages and vignettes. Here we provide a very brief overview:

• stan_lm, stan_aov,stan_biglm

  Similar to lm and aov but with novel regularizing priors on the model
  parameters that are driven by prior beliefs about R-squared, the proportion of
  variance in the outcome attributable to the predictors in a linear model.

• stan_glm, stan_glm.nb

  Similar to glm but with various possible prior distributions for the
  coefficients and, if applicable, a prior distribution for any auxiliary
  parameter in a Generalized Linear Model (GLM) that is characterized by a
  family object (e.g. the shape parameter in Gamma models). It is also possible
  to estimate a negative binomial model similar to the glm.nb function
  in the MASS package.

• stan_glmer, stan_glmer.nb, stan_lmer

  Similar to the glmer, glmer.nb, and lmer functions (lme4 package) in
  that GLMs are augmented to have group-specific terms that deviate from the
  common coefficients according to a mean-zero multivariate normal distribution
  with a highly-structured but unknown covariance matrix (for which rstanarm
  introduces an innovative prior distribution). MCMC provides more appropriate
  estimates of uncertainty for models that consist of a mix of common and
  group-specific parameters.

• stan_nlmer

  Similar to nlmer (lme4 package) package for nonlinear “mixed-effects”
  models, but flexible priors can be specified for all parameters in the model,
  including the unknown covariance matrices for the varying
  (group-specific) coefficients.

• stan_gamm4

  Similar to gamm4 (gamm4 package), which augments a GLM (possibly with
  group-specific terms) with nonlinear smooth functions of the predictors to
  form a Generalized Additive Mixed Model (GAMM). Rather than calling
  lme4::glmer like gamm4 does, stan_gamm4 essentially calls stan_glmer,
  which avoids the optimization issues that often crop up with GAMMs and
  provides better estimates for the uncertainty of the parameter estimates.

• stan_polr

  Similar to polr (MASS package) in that it models an ordinal response,
  but the Bayesian model also implies a prior distribution on the unknown
  cutpoints. Can also be used to model binary outcomes, possibly while
  estimating an unknown exponent governing the probability of success.

• stan_betareg

  Similar to betareg (betareg package) in that it models an outcome that
  is a rate (proportion) but, rather than performing maximum likelihood
  estimation, full Bayesian estimation is performed by default, with
  customizable prior distributions for all parameters.

• stan_clogit

  Similar to clogit (survival package) in that it models an binary outcome
  where the number of successes and failures is fixed within each stratum by
  the research design. There are some minor syntactical differences relative
  to survival::clogit that allow stan_clogit to accept
  group-specific terms as in stan_glmer.

• stan_mvmer

  A multivariate form of stan_glmer, whereby the user can specify
  one or more submodels each consisting of a GLM with group-specific terms. If
  more than one submodel is specified (i.e. there is more than one outcome
  variable) then a dependence is induced by assuming that the group-specific
  terms for each grouping factor are correlated across submodels.

• stan_jm

  Estimates shared parameter joint models for longitudinal and time-to-event
  (i.e. survival) data. The joint model can be univariate (i.e. one longitudinal
  outcome) or multivariate (i.e. more than one longitudinal outcome). A variety
  of parameterisations are available for linking the longitudinal and event
  processes (i.e. a variety of association structures).

The modeling functions in the rstanarm package take an algorithm
argument that can be one of the following:

• Sampling (algorithm="sampling"):

Uses Markov Chain Monte Carlo (MCMC) — in particular, Stan’s implementation
of Hamiltonian Monte Carlo (HMC) with a tuned but diagonal mass matrix —
to draw from the posterior distribution of the parameters. This is the slowest
but most reliable of the available estimation algorithms and it is the
default and recommended algorithm for statistical inference.

• Mean-field (algorithm="meanfield"):

Uses mean-field variational inference to draw from an approximation to the
posterior distribution. In particular, this algorithm finds the set of
independent normal distributions in the unconstrained space that — when
transformed into the constrained space — most closely approximate the
posterior distribution. Then it draws repeatedly from these independent
normal distributions and transforms them into the constrained space. The
entire process is much faster than HMC and yields independent draws but
is not recommended for final statistical inference. It can be useful to
narrow the set of candidate models in large problems, particularly when
specifying QR=TRUE in stan_glm, stan_glmer, and stan_gamm4, but is
only an approximation to the posterior distribution.

• Full-rank (algorithm="fullrank"):

Uses full-rank variational inference to draw from an approximation to the
posterior distribution by finding the multivariate normal distribution in
the unconstrained space that — when transformed into the constrained space
— most closely approximates the posterior distribution. Then it draws
repeatedly from this multivariate normal distribution and transforms the
draws into the constrained space. This process is slower than meanfield
variational inference but is faster than HMC. Although still an
approximation to the posterior distribution and thus not recommended
for final statistical inference, the approximation is more realistic than
that of mean-field variational inference because the parameters are not
assumed to be independent in the unconstrained space. Nevertheless, fullrank
variational inference is a more difficult optimization problem and the
algorithm is more prone to non-convergence or convergence to a local
optimum.

• Optimizing (algorithm="optimizing"):

Finds the posterior mode using a C++ implementation of the LBGFS algorithm. If
there is no prior information, then this is equivalent to maximum likelihood,
in which case there is no great reason to use the functions in the rstanarm
package over the emulated functions in other packages. However, if priors are
specified, then the estimates are penalized maximum likelihood estimates, which
may have some redeeming value. Currently, optimization is only supported for
stan_glm.